I think it would be a cool and interesting feature if new fish could be caught in caves. With the new aquifers, and lush caves having lots of water, it would be interesting to have more types of catchable fish, or underground loot tables.
Maybe you can breed axolotl with underground fish rather than buckets of tropical fish, which are difficult to aquire if you can't find a warm ocean.
Maybe you're more likely to catch treasure or junk underground, adding a bit of strategy to fishing with the extra incentive.
Perhaps these cave fish can be used for new potions, or give special effects when eaten. It would add to the immersion of the aquifers, and add something more to do in said aquifers.
You've also stated that you enjoy opening the game up to different play styles. Well, with the possibility of cave bases and playthroughs in the new update, having a strong and unique source of food in the caves may be very helpful.
Cave fish would also reward the player for exploring the caves. Cave fish would also allow for a stronger source of food underground than glow berries, so players who will be spending a large amount of time in the new caves won't have to worry about food if they run out.
They don't even necessarily have to be a mob too. In real life, many cave fish species are transparent. So, the logic might be that these elusive cave fish are invisible to the naked eye, and must be fished with a fishing rod.
It's a simple feature which will make the new caves that much more interesting to explore, create strategy to fishing locations, reward exploration of the new caves, and benefit different play styles. There's no reason not to add it.